NOSMO Methodologendag, vrijdag 6 juni 2008, Amsterdam

Sessie

onderzoeksgroep

Longitudinale Modellen (LOMO)

“Continue tijd modellering van panel data”

Analyse van panel data vindt bijna altijd plaats met
behulp van discrete-tijd methoden. Vanwege
de doorgaans grote observatie-intervallen in panel onderzoek (een à twee
keer per jaar of zelfs minder frequent) is de gebruikelijke discrete-tijd
analyse echter problematisch. Ongelijke intervallen maken vergelijking van de
resultaten tussen en binnen onderzoeken onmogelijk. Maar zelfs bij gelijke
intervallen impliceren gelijke discrete-tijd effecten niet dat de onderliggende
continue-tijd effecten gelijk zijn. De bijdragen aan de sessie laten op
verschillende manieren zien, hoe de valkuilen van een discrete-tijd analyse
kunnen worden vermeden.

**13.30-14.00** **Christian Steglich &
Tom Snijders**

* Continuous-Time
Models forComplete Social Networks*

14.00-14.30
Marc Delsing & Han Oud

* Analyzing Reciprocal Relationships by Means
of the*

*Continuous-Time
Autoregressive Latent Trajectory (CALT) Model*

14.30-15.00
Zita Oravecz & Francis Tuerlinckx

*Analyzing
Intensive Longitudinal Data with a Latent Stochastic Model*

15.00-15.15 Pauze

**15.15-15.45
Han Oud & Henk Folmer**

*Spatial Econometric Methods in Continuous Time Modeling
of Panel Data with Latent Variables*

Abstracts

Continuous-Time Models for
Complete Social Networks

**Christian Steglich**

c.e.g.steglich@rug.nl

**Tom Snijders**

*Faculty of Behavioural and Social Sciences*

*University** of Groningen*

In many applied
social science disciplines, dynamics of complete social networks currently
receive a lot of attention -- be it friendship networks among school children,
or collaboration networks among firms. Although continuous-time process tracing
data become increasingly available due to computer-assisted data collection,
the most

common data
format still is the panel design. Here, for a fixed group of actors, the
complete network of social ties among them is assessed in a series of discrete
observations over time. Differences between observation moments typically are
very complex and difficult to model. Moreover, they usually can be explained by
multiple, competing dynamic mechanisms. A continuous time modelling approach is
introduced that enables researchers to decompose the observed total change into
a stochastic sequence of smaller changes that are easier to model. In this
framework, it also is easier to formulate hypotheses that test the alternative
theoretical mechanisms. The approach comes at the cost of conditional
independence assumptions typical for stochastic process models. As an example,
the co-evolution of friendship networks at school and smoking uptake of the
pupils is analysed. The proposed methods are implemented in the

**Analyzing
Reciprocal Relationships by Means of the**

**Continuous-Time
Autoregressive Latent Trajectory (CALT) Model**

**Marc Delsing**

m.delsing@uu.nl

*Research** Center*

*Utrecht** University*

**Han Oud**

*Behavioural Science
Institute*

*Radboud University Nijmegen*

Over the past decades, several analytic tools have become available for the analysis of reciprocal relations in a non-experimental context using structural equation modeling (SEM). A recently proposed model is the autoregressive latent trajectory (ALT) model (Bollen and Curran, 2004, Curran and Bollen, 2001), which captures features of both the autoregressive (AR) cross-lagged model and the latent trajectory (LT) model. In this presentation, strengths and weaknesses are discussed and it is demonstrated how several of the problems can be solved by a continuous time version: continuous time autoregressive latent trajectory (CALT) model. The EDM/SEM continuous time procedure, using SEM to estimate the exact discrete model (EDM), is applied to a CALT model of reciprocal relations between antisocial behavior and depressive symptoms.

**Analyzing
Intensive Longitudinal Data with a Latent Stochastic Model**

**Zita Oravecz**

zita.oravecz@psy.kuleuven.be

**Francis Tuerlinckx**

*Research Group
Quantitative and Personality Psychology*

*Leuven University*

Social sciences often aim to explore the within subject variation of certain quantities by repeatedly measuring them. Moreover, understanding the difference among individuals with respect to these variations has become a central issue. The talk describes an approach which incorporates both problems in a dynamical model. First of all, it takes advantage of a continuous time stochastic process, namely the Ornstein-Uhlenbeck process, to model the underlying dynamics in the longitudinal data of one individual. The approach involves simultaneous modelling of longitudinal variables; hence their dependency structure can also be explored. Second, a hierarchical extension of this core model is developed, allowing a complex investigation of interindividual differences for a group of individuals. For instance, the autocorrelation of the underlying process can be turned into a random effect. Furthermore, covariates can be introduced so that interindividual differences can be studied in many respects. The model can handle unbalanced datasets and is especially fit for the analysis of relatively long repeated measurement chains of several individuals. As an illustration, an application on a dataset collected in a diary study will also be presented.

**Spatial
Econometric Methods in Continuous Time Modeling of Panel Data with Latent Variables**

**Han Oud**

j.oud@pwo.ru.nl

*Behavioural Science
Institute*

*Radboud** University
*

**Henk Folmer**

*Department of Spatial
Sciences, *

* Department of Social Sciences, *

There are compelling arguments for continuous time modeling of panel data (see, e.g., special issue 62:1, 2008, of Statistica Neerlandica). Most social phenomena evolve in continuous time and analysis in discrete time (cross-lagged panel analysis) oversimplifies and even distorts reality. Discrete time analysis especially gets in trouble, when the observation intervals are unequal both within and between studies. A not less compelling reason for analyzing cross-effects in continuous time is that equal effects found in discrete time do not guarantee at all that the underlying continuous time effects are equal. So, even in the case of equal observation intervals, discrete time analysis proves to be useless. The cross-lagged effects found in discrete time in fact are part of an ongoing process and one should conclude on the basis of the cross-lagged effect functions across time instead of the discrete time interval only.

Spatial econometrics has been developed to analyze data, for which the central assumption of independence is not applicable. This is clear especially for spatial data, because less distant observation units in general will show higher correlation than more distant units. This kind of dependence is in no way restricted to spatial data, however, but often also present in survey data. We introduce spatial econometric methods for solving the unit dependence problem into the latent variable framework and the continuous time modeling of panel data. The methodology will be applied to German unemployment data over 4 years (200, 2001, 2002, 2003) in 439 regions.